'Storage Device - Cell - Storage Device' Structure Modeling

摘要

The article presents the semi-Markov model of a structure "input storage device - a service device - an output storage device". Partitioning of a plurality of states into subsets is performed describing the failure-free operation of the system to receive or deliver products. We determine the residence times of the system in states with the allowance for repeated hits using the theorem on the distribution functions of the residence times for the system in states with the allowance for repeated hits for which the coefficients of increasing the residence time of the system in states due to repeated hits in them are found. While using the trajectory method, the functions of distributing the fail-safe times for product acceptance and give-away by such a structure is determined for the times of the system presence in the trajectories of the system's exit from a subset of states describing the failure-free operation of the system for receiving or issuing products and the probability of these trajectories implementation are found. The mathematical expectation of this structure uptime for receiving and for output of the products obtained as a result of modeling and the average time of the system stay in a subset of states are compared. While comparing the simulation results, it was assumed that the random variables characterizing the given system are distributed according to the generalized Erlang law of the second order and have continuous functions and distribution densities.